Discrete-Time Flocking Control in Multi-Robot Systems With Random Link Failures

The stability of multi-robot flocking is closely related to the control model and the quality of wireless communications. In this study, we delve into the discrete-time flocking control problem for multi-robot systems (MRS) operating under an ad hoc network with random link failures. Specifically, we initially propose a discrete-time control model for multi-robot flocking that describes the inherent instability in the transmission of robot state information as a Bernoulli variable. Compared to existing controllers, this model requires less information exchange and is more practical for implementation in multi-robot systems. Subsequently, stability analysis is conducted for the controller, revealing that the MRS cannot achieve asymptotic flocking but can attain flocking in expectation when relevant stability conditions are satisfied. The stability conditions are deduced using the Lyapunov method, imposing constraints on the controller gains, the interaction period, and the successful transmission probability of communication links. Notably, the upper bound for the interaction period is significantly improved, thereby alleviating the communication network's burden. Simulation results verify the efficacy of the proposed control model and the reliability of the derived stability conditions.